On The Spectrum Of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition I. Necessary Conditions

1965 ◽  
Vol 10 (1) ◽  
pp. 85-106 ◽  
Author(s):  
I. A. Ibragimov
Keyword(s):  
Necessary Conditions ◽  
Strong Mixing ◽  
Mixing Condition ◽  
Strong Mixing Condition

A nearly independent, but non-strong mixing, triangular array

1985 ◽  
Vol 22 (03) ◽  
pp. 729-731 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Random Variables ◽  
Triangular Array ◽  
Strong Mixing ◽  
Common Condition ◽  
Mixing Condition ◽  
First Order ◽  
Triangular Arrays ◽  
The Central Limit Theorem ◽  
Independent Identically Distributed ◽  
Strong Mixing Condition

The condition of strong mixing for triangular arrays of random variables is a common condition of weak dependence. In this note, it is shown that this condition is not as general as one might believe. In particular, it is shown that there exist triangular arrays of first-order autoregressive random variables which converge almost surely to an independent identically distributed sequence of random variables and for which the central limit theorem holds, but which are not strong mixing triangular arrays. Hence, the strong mixing condition is more restrictive than desired.

PROBABILITY DISTRIBUTIONS OF SCATTERED SIGNALS IN A RANDOM MULTILAYER

2007 ◽  
Vol 07 (04) ◽  
pp. R49-R61
Author(s):  
J. -H. KIM
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Turning Point ◽  
Review Paper ◽  
Probability Distributions ◽  
Strong Mixing ◽  
Random Wave ◽  
Mixing Condition ◽  
Asymptotic Formulation ◽  
Strong Mixing Condition

This is a review paper on the study of the randomly scattered signals in a random multilayer based upon a stochastic and asymptotic formulation under strong mixing condition. This formulation generalizes the dominant Ito's formulation. The existence of a turning point of the random wave requires several type stochastic differential equations and the relevant limit theorems. The probability distributions of the randomly scattered signals have been obtained in the form of the Kolmogorov PDEs along the line of Khasminskii's limit theorem. This article demonstrates the step-by-step development of the relevant generators which contain the ultimate information for the probability distributions of the random signals.

scholarly journals On the strong attraction of functions on dependent variables to the normal law

2020 ◽  
pp. 5-19
Author(s):  
A. G. Grin
Keyword(s):  
Symmetric Functions ◽  
Random Variables ◽  
Strong Mixing ◽  
Stationary Sequences ◽  
Mixing Condition ◽  
Strong Attraction ◽  
Dependent Variables ◽  
Normal Law ◽  
Strong Mixing Condition ◽  
General Conditions

For symmetric functions on random variables from stationary sequences satisfying the uniformly strong mixing condition, the general conditions of attraction to the normal law in terms of distributions of individual items are obtained. The main result of the paper generalizes all known to present results of this type.

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